can dhcp work in two different virtual s

we outgrew our first subnet range of 192.168.1.0 and we were given another subnet range of 192.168.4.0 these both are on the inside of a router that uses nat so our dhcp will not have to cross a router. we installed a dhcp server on a server that resides in the first range of 192.168.1.0 but because we were out of addresses in that range we created a scope of addresses that was in the range of 192.168.4.0. when we tried to log on and get an address from the dhcp machine we did not it. I am wondering if dhcp will work when configured like this.